1. Which is the most
simplified form of
?
2. What is the
simplified form of 3log 2 – log 4?
A
|
log
2
|
B
|
log (3/2)
|
C
|
log
4
|
D
|
log 32
|
3. Which is
equivalent to log2 (5/6)
?
A. log2
5 + log2 6
B.
log2 5 – log2 6
C.
log2 5 ÷ log2 6
D. log2
5 × log2 6
4. What does 0.5
represent in
?
A.
50%
decrease
B. 50% increase
C. initial value
D.
y-intercept
5. What does the
number 6 represent in the following equation: y = 6(1.04)x?
A
|
6
% decrease
|
B
|
6
% increase
|
C
|
initial
value
|
D
|
x-intercept
|
6. After two years you had $137.81 in an
account, and after 4 years you had $151.94. What is your approximate annual
interest rate?
A
|
5%
|
B
|
10.2%
|
C
|
1.05%
|
D
|
1.102%
|
7. Which is the asymptote in the graph of y = log(x – 5) + 2
?
A
|
y = 2
|
B
|
x = 5
|
C
|
y = −2
|
D
|
x = −5
|
8. Where is the
asymptote in the graph of the equation y
= 5 + 2 log(x – 3)?
A
|
x = −3
|
B
|
x = 3
|
C
|
y = 5
|
D
|
y = −5
|
9. When solving the logarithmic equation ,
which
represents the correct second step in the solution process?
10. Solve for x using the change of base formula: 5x – 1 = 100
A
|
3.86
|
B
|
2.87
|
C
|
.349
|
D
|
1.349
|
11. Water is boiled to 100°C for a cup of tea. Five minutes later the tea is 88°C. The room temperature is 25°C. Which value represents the asymptote?
12. Water is boiled to 100°C for a cup of tea. Five minutes later the tea is 88°C. The room temperature is 25°C. At what rate is the tea cooling?
A
|
84%
|
B
|
96.6%
|
C
|
3.4%
|
D
|
1.034%
|
Multiple-Choice Answer Key
1. B
|
2. A
|
3. B
|
4. A
|
5. C
|
6. A
|
7. B
|
8. B
|
9. C
|
10. A
|
11. D
|
12. C
|
|
|
|
Short-Answer Items:
13. Simplify
. Show at least two steps.
14. A colony of bacteria began with 500. After 5
days there were 235. At what rate are the bacteria dying?
15. Graph the following logarithmic function: y = 2 – 4log9 (x – 1) and label all important
components. Provide the domain and range.
16. The black bear population is growing. A study
shows that there were 34 bears after 4 years and 57 bears after 8 years. How
many bears were there when the study began?
Short-Answer Key and Scoring
Rubrics:
13. Simplify
. Show at least two steps.
Scoring Rubric for Item 13
Points
|
Description
|
3
|
·
The student writes the correct simplification
of 3x and shows at least two steps.
|
2
|
·
The student writes the correct simplification
of 3x and shows at least one step.
|
1
|
·
The student writes the correct simplification
of 3x, but does not show any steps.
|
0
|
·
The student does not provide an answer or
writes the incorrect simplification.
|
14. A colony of bacteria began with 500. After 5
days there were 235. At what rate are the bacteria dying? 14%
15. Graph the following logarithmic function: y = 2 – 4log9 (x – 1) and label all important
components. Provide the domain and range.)
Scoring Rubric for Item 15
Points
|
Description
|
3
|
·
The graph has all of the following:
o
axes are labeled
o
vertical asymptote at x = 1 and is labeled
o
x-intercept
at (3, 0) and is labeled
o
domain (–2 ≤ x ≤ 4) and range(0 ≤ y)
are stated
|
2
|
·
A graph is made but some parts are incorrect
or unlabeled.
|
1
|
·
A graph is made but not labeled.
|
0
|
·
The student’s response is incorrect,
irrelevant, too brief to evaluate, or missing.
|
16. The black bear population is growing. A study
shows that there were 34 bears after 4 years and 57 bears after 8 years. How
many bears were there when the study began?
20 bears
Write a mini-mystery that would require using exponential and logarithmic
functions to solve. Set the mystery up and then show your work to solve it. Use
tables, graphs, and equations, as well as full sentences in your explanations.
Points
|
Description
|
4
|
·
The student’s mystery requires using
exponential and logarithmic functions to solve. The student’s work has the
following five components:
o
an equation that represents the situation
o
a table of values
o
a graph that represents the situation
o
all the steps to solving the mystery
o
explanatory sentences (describing the mystery
and how to solve it)
|
3
|
·
The student’s work has four of the five
necessary components.
|
2
|
·
The student’s work has three of the five
necessary components.
OR
·
The student provides all necessary information
except for how to solve the mystery.
|
1
|
·
The student’s work has two of the five
necessary components.
OR
·
The student explains the mystery and how to
solve it but does not provide the necessary visuals: equation, table, graph.
|
0
|
·
The student’s response is incorrect,
irrelevant, too brief to evaluate, or missing.
|